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<td>Re: Biologic - at the interface between biology,
topology, logic and cybernetics.</td>
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<th valign="BASELINE" align="RIGHT" nowrap="nowrap">Fecha: </th>
<td>Fri, 3 Jan 2025 12:38:13 -0600</td>
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<th valign="BASELINE" align="RIGHT" nowrap="nowrap">De: </th>
<td>Louis Kauffman <a class="moz-txt-link-rfc2396E" href="mailto:loukau@gmail.com"><loukau@gmail.com></a></td>
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<td>"Pedro C. Marijuán" <a class="moz-txt-link-rfc2396E" href="mailto:pedroc.marijuan@gmail.com"><pedroc.marijuan@gmail.com></a></td>
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<div class="" align="center"><font size="4"><b>Biologic - at
the interface between biology, topology, logic and
cybernetics.</b></font></div>
<div class="" align="center"><font size="4"><b><br>
</b></font></div>
<div class="" align="center"><b>Louis H Kauffman, UIC</b></div>
<div class=""><br class="">
</div>
<div class="" align="center">“What can be shown, cannot be
said.”</div>
<div class="" align="center">“Was gezeigt werden kann, kann
nicht gesagt werden.”</div>
<div class="" align="center">(Wittgenstein, Tractatus,
4.1212)</div>
<div class="" align="center"><br class="">
</div>
<div class="" align="center">“We take the form of
distinction for the form.”</div>
<div class="" align="center">(Spencer-Brown, Laws of Form,
Chapter 1)</div>
<div class=""><br class="">
</div>
<div class="">What is the form of biology?</div>
<div class="">Is there a biology of form?</div>
<div class=""><br>
</div>
<div class="">In particular, this is a study of different
forms and formalisms for replication. We concentrate on
diagrammatic formal systems not only for the sake of
showing how there may be fundamental mathematical
structure in biology, but also to consider philosophical
and phenomenological points of view in relation to natural
science and mathematics. The relationship with
phenomenology comes about in the questions that arise
about the nature of the observer in relation to the
observed that arise in philosophy, but also in science in
the very act of determining the context and models upon
which it shall be based. Our original point of departure
was the idea of distinction and cybernetic epistemology.
Cybernetic epistemology has much to say about the relation
of the self to structures that may harbor a self. What is
the interlacement of selves and organisms?</div>
<div class=""> </div>
<div class="">Our point of view is structural. There is a
distinct difference between building up structures in
terms of principles and imagining that models of the world
are constructed from some sort of building-bricks. I want
to make this point as early as possible because in
mathematics one naturally generates hierarchies, but that
does not make the mathematician a reductionist. We think
of geometry as the consequences of certain axioms for the
purpose of organizing our knowledge, not to insist that
these axioms are in any way other than logically prior to
the theorems of the system. Just so, we look for
fundamental patterns from which certain complexes of
phenomena and ideas can be organized. This does not entail
any assumption about ``the world'' or how the world may be
built from parts. What is a part that a world might be
built from it?</div>
<div class=""><br class="">
</div>
<div class="">We examine the schema behind the reproduction
of DNA. The pattern of the DNA reproduction is very
simple. The DNA molecule consists of two interwound
strands, the Watson Strand (W) and the Crick Strand (C).
The two strands are bonded to each other via a backbone of
base-pairings and these bonds can be broken by certain
enzymes present in the cell. In reproduction of DNA the
bonds between the two strands are broken and the two
strands then acquire the needed complementary base
molecules from the cellular environment to reconstitute
each a separate copy of the DNA. At this level the
situation can be described by a symbolism like this.</div>
<div class="">DNA = <W|C> -----> <W| E |C>
-----> <W|C> <W|C> = DNA DNA.</div>
<div class="">Here E stands for the environment of the cell.
The first arrow denotes the separation of the DNA into the
two strands. The second arrow denotes the action between
the bare strands and the environment (the creation of new
base-pairings) that leads to the production of the two DNA
molecules.</div>
<div class=""><br class="">
</div>
<div class="">Much is left out of this schema. Indeed the
DNA molecule is a tight spiral winding of its two
interlocked strands and so the new DNA's would be linked
around one another if it were not for the work of
toposomerase enzymes that manage to unlink the new DNA's
in time for cell division to occur. Nevertheless, this is
the large scale description of the replication of DNA that
is fundamental to the division of cells and to the
continuance of living organisms.</div>
<div class=""><br class="">
</div>
<div class="">This form of replication can be compared with
other forms. For example, John von Neumann suggested a
“building machine” B such that when B is supplied with a
“blueprint” x then </div>
<div class="">B, x —> B,x , X,x</div>
<div class="">This means that B and the blueprint x will
produce X the entity whose plan is x along with a copy of
the blueprint x. The first B,x is the persistence of the
original machine B.</div>
<div class="">Let b be the blueprint for B itself. Then</div>
<div class="">B,b —> B,b , B,b.</div>
<div class="">The Von Neumann Machine replicates itself. </div>
<div class="">In the comparison, we see that The DNA
contains (in its strands) the blueprint for its own
replication.</div>
<div class=""><br class="">
</div>
<div class="">The comparison made, what questions do you
ask? The mathematical roots of von Neumann’s construction
are very deep. What are the physical/biological roots of
the DNA replication?</div>
<div class=""><br class="">
</div>
<div class="">We invite the reader to examine the form of
the science involved in this well-known description. We
speak of the DNA molecules as though we could see them
directly in the phenomenology of our ordinary sight.
Science does involve the direct extension of sight as the
experience of looking through a telescope or a light
microscope. But in the case of the DNA one proceeds by
logical consistency and the indirect but vivid images via
the electron microscope and the patterns of gel
electrophoresis. In the case of electron microscope images
there is every reason to assume (it appears consistent to
assume) that the objects shown can be taken to be
analogous to the macroscopic objects of our perception.
This means that one has the possibility of observing
``directly" that DNA molecules can be knotted. I do not
say that one can observe directly the coiling of the
Watson and the Crick strands, but the DNA can be observed
as though it were a long rope. This rope can be seen to be
coiled and knotted in electron micrographs. Even this
``showing'' requires a difficult technique beyond the
usual techniques of the electron microscope. The DNA was
coated with protein by the experimenters so that it became
a chain of larger and more robust diameter. Then the
electron microscope revealed the patterns of knotting in
an apparent projection of the coated DNA from three
dimensional space to the two dimensional space of the
image.</div>
<div class=""><img apple-inline="yes"
id="093308C2-C64C-41FE-8115-2651F174960D"
src="cid:part1.Pi9sV3qA.r60UBYyM@gmail.com" class=""></div>
<div class=""><br class="">
</div>
<div class="">It is remarkable how consistent is the
hypothesis of indirect perception on which the work is
based. Most working biologists would not question the
basis of their biological perceptions direct or indirect.
For those who are philosophically inclined there is a
lesson to be learned about experimental phenomenology. </div>
<div class="">One wants to know how far a world-view can be
extended before it disintegrates.</div>
<div class="">What we see in the electron micrograph is
deeply shaped by the complex story of biological
experiment that surrounds it.</div>
<div class=""> </div>
<div class="">Along with these forays into experimentation,
there are analogous forays into the limits of logic. Here
we meet the replication schema again. Replication in logic
is intimately related to self-reference and to formalisms
that can lead to paradox. The reasons for this are, by
now, apparent. The usual mathematical formalisms for set
theory assume that there is no temporal evolution in the
structures. </div>
<div class="">Temporality may look like a tragedy for the
classical mathematics, but it is exactly what interests us
when studying biology. </div>
<div class="">Mathematical biology is concerned with those
structures leading to recursive generation of structures
from themselves and from their environments. </div>
<div class=""> </div>
<div class="">#############################</div>
<div class=""><br class="">
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<div class="">Here is a related paper:</div>
<div class=""><a href="https://urldefense.com/v3/__https://arxiv.org/abs/1512.04325__;!!D9dNQwwGXtA!Xuz20L8dnuTZYF9WFBHOLyZrvHTyVKqbCy4P55woe-bSQswWK6oGtDnIfdh8ErbhHvbI71N24gtkTUTyEMIjViUloF5d$" class="moz-txt-link-freetext" moz-do-not-send="true">https://arxiv.org/abs/1512.04325</a></div>
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<div class="">Very best,</div>
<div class="">Louis H Kauffman</div>
<div class="">Dept Mathematics</div>
<div class="">University of Illinois at Chicago</div>
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